Details

Time bar (total: 6.5s)

sample51.0ms

Algorithm
intervals
Results
28.0ms282×body80valid
7.0ms72×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize119.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-log-exp
9×add-cube-cbrt
6×pow1 sqrt-prod
4×add-exp-log expm1-log1p-u distribute-rgt-neg-in sqrt-div add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg flip3-+ fma-neg diff-log prod-diff neg-log flip-+
Counts
4 → 77
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify134.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0264600
11046558
24657542
35001542

prune383.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.8b

localize119.0ms

Local error

Found 4 expressions with local error:

8.5b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 88
Calls
4 calls:
13.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify180.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02831391
19981121
247231013
350011013

prune460.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.8b

localize123.0ms

Local error

Found 4 expressions with local error:

22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
100.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0215657
1688619
22689612
35001611

prune417.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.8b

localize131.0ms

Local error

Found 4 expressions with local error:

22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.5b
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
23.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
220×cbrt-div
190×sqrt-div
136×frac-times
111×flip3-- flip--
50×associate-*l/
44×associate-*r/
15×pow1
9×pow-prod-down
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod sqrt-pow1 pow1/3
4×add-exp-log expm1-log1p-u sqrt-prod add-cbrt-cube log1p-expm1-u add-log-exp
2×pow1/2
1×rem-sqrt-square
Counts
4 → 143
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
122.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series355.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
107.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
101.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify150.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
08376098
117666045
243135801
350015801

prune788.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.8b

regimes202.0ms

Accuracy

90.6% (1.2b remaining)

Error of 8.8b against oracle of 7.6b and baseline of 20.3b

bsearch201.0ms

Steps
ItersRangePoint
8
6.881289457293598e+137
5.567978725714423e+140
9.254035461668974e+137
9
-4.598976243999122e+69
-2.027222800079687e+63
-2.968512005892858e+66

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05464
15464

end0.0ms

sample1.4s

Algorithm
intervals
Results
892.0ms8735×body80valid
263.0ms2915×body80nan